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Mirrors > Home > MPE Home > Th. List > elpredg | Structured version Visualization version Unicode version |
Description: Membership in a predecessor class. (Contributed by Scott Fenton, 17-Apr-2011.) |
Ref | Expression |
---|---|
elpredg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pred 5680 | . . . . 5 | |
2 | 1 | elin2 3801 | . . . 4 |
3 | 2 | baib 944 | . . 3 |
4 | 3 | adantl 482 | . 2 |
5 | elimasng 5491 | . . 3 | |
6 | df-br 4654 | . . 3 | |
7 | 5, 6 | syl6bbr 278 | . 2 |
8 | brcnvg 5303 | . 2 | |
9 | 4, 7, 8 | 3bitrd 294 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wcel 1990 csn 4177 cop 4183 class class class wbr 4653 ccnv 5113 cima 5117 cpred 5679 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 |
This theorem is referenced by: predpo 5698 predpoirr 5708 predfrirr 5709 wfrlem10 7424 wsuclem 31773 wsuclemOLD 31774 wsuclb 31777 |
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